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We explore the evolution of the internal gas kinematics of star-forminggalaxies from the peak of cosmic star-formation at $z\sim2$ to today.Measurements of galaxy rotation velocity $V_{rot}$, which quantify orderedmotions, and gas velocity dispersion $\sigma_g$, which quantify disorderedmotions, are adopted from the DEEP2 and SIGMA surveys. This sample covers acontinuous baseline in redshift from $z=2.5$ to $z=0.1$, spanning 10 Gyrs. Atlow redshift, nearly all sufficiently massive star-forming galaxies arerotationally supported ($V_{rot}>\sigma_g$). By $z=2$, the percentage ofgalaxies with rotational support has declined to 50$\%$ at low stellar mass($10^{9}-10^{10}\,M_{\odot}$) and 70$\%$ at high stellar mass($10^{10}-10^{11}M_{\odot}$). For $V_{rot}\,>\,3\,\sigma_g$, the percentagedrops below 35$\%$ for all masses. From $z\,=\,2$ to now, galaxies exhibitremarkably smooth kinematic evolution on average. All galaxies tend towardsrotational support with time, and it is reached earlier in higher mass systems.This is mostly due to an average decline in $\sigma_g$ by a factor of 3 since aredshift of 2, which is independent of mass. Over the same time period,$V_{rot}$ increases by a factor of 1.5 for low mass systems, but does notevolve for high mass systems. These trends in $V_{rot}$ and $\sigma_g$ withtime are at a fixed stellar mass and should not be interpreted as evolutionarytracks for galaxy populations. When galaxy populations are linked in time withabundance matching, not only does $\sigma_g$ decline with time as before, but$V_{rot}$ strongly increases with time for all galaxy masses. This enhances theevolution in $V_{rot}/\sigma_g$. These results indicate that $z\,=\,2$ is aperiod of disk assembly, during which the strong rotational support present intoday's massive disk galaxies is only just beginning to emerge.

z~2: An Epoch of Disk Assembly